| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Moderate -0.3 This is a standard M1 velocity-time graph question requiring area calculations (distance = area under graph), use of average speed formula, and solving simultaneous equations. While multi-part with several steps, it follows a routine template with clear guidance ('show that') and uses straightforward mechanics concepts without requiring novel insight or complex problem-solving. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks |
|---|---|
| (a) Total distance \(=\) sum of areas \(= 4x + 64 + 24y + 18y + 42\) | M1 A1 |
| Hence \(4x + 42y + 106 = 496\) | M1 A1 |
| \(2x + 21y = 195\) | |
| (b) Total time \(= x + 2y + 11\), so \(496 = 15.5(x + 2y + 11)\) | M1 A1 |
| \(x + 2y + 11 = 32\) | |
| \(x + 2y = 21\) | A1 |
| (c) Solving: \(x = 3\), \(y = 9\) | M1 A1 A1 |
| (d) \(\frac{8}{3}, 4, 0, -\frac{4}{3}, -\frac{12}{7} \text{ ms}^{-2}\) | B3 |
| Total: 13 marks |
(a) Total distance $=$ sum of areas $= 4x + 64 + 24y + 18y + 42$ | M1 A1 |
| Hence $4x + 42y + 106 = 496$ | M1 A1 |
| $2x + 21y = 195$ | |
(b) Total time $= x + 2y + 11$, so $496 = 15.5(x + 2y + 11)$ | M1 A1 |
| $x + 2y + 11 = 32$ | |
| $x + 2y = 21$ | A1 |
(c) Solving: $x = 3$, $y = 9$ | M1 A1 A1 |
(d) $\frac{8}{3}, 4, 0, -\frac{4}{3}, -\frac{12}{7} \text{ ms}^{-2}$ | B3 |
| | **Total: 13 marks**The velocity-time graph illustrates the motion of a particle which accelerates from rest to 8 ms$^{-1}$ in $x$ seconds and then to 24 ms$^{-1}$ in a further 4 seconds. It then travels at a constant speed for another $y$ seconds before decelerating to 12 ms$^{-1}$ over the next $y$ seconds and then to rest in the final 7 seconds of its motion.
\includegraphics{figure_6}
Given that the total distance travelled by the particle is 496 m,
\begin{enumerate}[label=(\alph*)]
\item show that $2x + 21y = 195$. [4 marks]
\end{enumerate}
Given also that the average speed of the particle during its motion is 15.5 ms$^{-1}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item show that $x + 2y = 21$. [3 marks]
\item Hence find the values of $x$ and $y$. [3 marks]
\item Write down the acceleration for each section of the motion. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [13]}}